Method and apparatus for reconstructing image and medical image system employing the method

ABSTRACT

A method and apparatus for reconstructing an image and a medical image system are provided. An image reconstruction processing method may include acquiring an initial value with respect to a tomographic image of an object to be inspected, initializing an auxiliary variable, acquiring one or both of a weighted value and an error value, based on a measured value, transforming a measured image signal, updating the auxiliary variable using a transform coefficient used to transform the measured image signal, and updating the measured value using the updated auxiliary variable, and one or both of the acquired weighted value and the error value.

CROSS-REFERENCE TO RELATED APPLICATION

This application is a Divisional Application of U.S. application Ser.No. 13/223,707, filed Sep. 1, 2011, which claims the benefit of KoreanPatent Application No. 10-2010-0087502, filed on Sep. 7, 2010, in theKorean Intellectual Property Office, the entire disclosure of which isincorporated herein by reference for all purposes.

BACKGROUND

1. Field

The following description relates to an image reconstruction method andapparatus, and a medical image system employing the image reconstructionmethod and apparatus.

2. Description of the Related Art

X-ray mammography is widely used to process an image of an internalorgan, for example, to process an image of breast tissues. For example,a Full Field Digital Mammography (FFDM) is believed by some as a costeffective approach to detect a microcalcification tissue with anextremely small size. In X-ray mammography, however, performance may bedegraded when detecting a mass that is one of main lesions. In the caseof breast examination, a radiation image for a breast may be obtained bycompressing tissues in the breast, and by performing two-dimensional(2D) projection. Here, however, when a density is high, it may bedifficult to perform an accurate diagnosis, since a large number oftissues appear to overlap each other.

A Digital Breast Tomosynthesis (DBT) scheme may be used to capture anobject to be inspected, for example, a breast, from 7 to 30 differentangles, in a different manner from the X-ray mammography. Thus, the DBTscheme may improve the overlapping of tissues issue.

A Computerized Tomography (CT) scheme may enable a three-dimensional(3D) reconstruction, since projection data for an angle greater than180° is obtained. Here, a Filtered Back-Projection (FBP) may be used asa reconstruction algorithm, and simple filtering is performed in theFourier domain and a back projection for combination in an image domainis performed.

In a tomographic image, that is, an image acquired under a tomosynthesisscheme, information may be lost as images are acquired in a limitedangle range.

A large number of X-ray systems display an image using a detectedattenuation characteristic by passing an X-ray with a single energy bandthrough an object to be inspected. When materials of the object havedifferent attenuation characteristics, an image in high quality may beobtained. However, when the materials of the object have similarattenuation characteristics, the quality of the image may bedeteriorated.

A multi-energy X-ray based system may acquire an X-ray image with atleast two energy bands. Generally, since materials exhibit differentX-ray attenuation characteristics in different energy bands, images maybe discriminated for each material based on the different X-rayattenuation characteristics.

Currently, with regards to CT schemes or nondestructive inspectiondevices, products equipped with a dual energy source or a dual energyseparation detector are being launched. The products may acquire animage by rotating a source by at least 180° on an object to be inspectedand accordingly, it is possible to obtain density images of materialsforming the object. A dual energy CT equipment may be used to obtain animage with a constant quality in a relatively simple manner, forexample, by masking Pseudo-color by adding, subtracting, or segmentingan acquired image.

In 3D reconstruction, a beam hardening artifact may occur due toapproximation of monochromatic radiation. An inner portion of an objectto be inspected may appear abnormally dark due to the beam hardeningartifact. In other words, reconstruction is performed by moreconsiderable attenuations in an outer portion of the object, and thusthe dark inner portion of the object may be interpreted as a phenomenondue to approximation of monochromatic radiation.

As described above, a system associated with a multi-energy X-ray usingat least two different energy spectrums has been proposed. Inreconstruction using the system, approximation of monochromaticradiation may be used.

SUMMARY

In one general aspect, there is provided a system associated with amulti-energy X-ray using at least two different energy spectrums, inwhich approximation of monochromatic radiation is not used, to improvethe accuracy of reconstruction.

In another aspect, there is provided a system associated with amulti-energy X-ray, in which a polychromatic radiation model is appliedin a quantitative material discrimination.

In still another aspect, there is provided an image reconstructionprocessing method, the method including acquiring an initial value withrespect to a tomographic image of an object to be inspected,initializing an auxiliary variable, acquiring one or both of a weightedvalue and an error value, based on a measured value, transforming ameasured image signal, updating the initialized auxiliary variable usinga transform coefficient used to transform the measured image signal, andupdating the measured value using the updated auxiliary variable, andone or both of the acquired weighted value and the error value.

The acquiring of one or both of the weighted value and the error valuemay include computing one or both of the weighted value and the errorvalue based on a secondary Taylor series approximation of aKullback-Leibler (KL) divergence function corresponding to a Poissonlog-likelihood function.

The acquiring of one or both of the weighted value and the error valuemay include computing one or both of the weighted value and the errorvalue, using one or more of a maximum likelihood-expectationmaximization (ML-EM) algorithm based on a monochromatic radiation model,an ML-convex algorithm, and a simultaneous algebraic reconstructiontechnique (SART) algorithm.

The transforming of the measured image signal may include transformingthe measured image signal to enable a multi-resolution analysis.

The transforming of the measured image signal to enable themulti-resolution analysis may include transforming the measured imagesignal using one or more of a wavelet transform, a contourlet transform,a curvelet transform, a shearlet transform, a bandelet transform, and aridgelet transform.

The updating of the auxiliary variable may include multiplying atransform coefficient of the measured value by a first weighted valuefor each portion, performing a gradient operation on the transformcoefficient multiplied by the first weighted value, and multiplying thetransform coefficient where the gradient operation is performed, by asecond weighted value, and adding the auxiliary variable thereto.

The updating of the measured value may include performing a divergenceoperation on the updated auxiliary variable, multiplying the auxiliaryvariable where the divergence operation is performed by a first weightedvalue for each portion, transforming the auxiliary variable multipliedby the first weighted value into an image signal, and multiplying avalue obtained by subtracting a value resulting from the transforming ofthe auxiliary variable from the acquired error value, by a secondweighted value, and adding the measured value thereto.

The method may further include repeating the acquiring of one or more ofthe weighted value and the error value, the transforming of the measuredimage signal, the updating of the initialized auxiliary variable, andthe of updating the measured value.

In still another aspect, there is provided a material discriminationimage generator, the image generator including an initial imageestimator configured to receive a projection image for each energy bandgenerated by passing a multi-energy X-ray spectrum through an object tobe inspected having at least one material, and to generate an initialimage for each of the at least one material, and an image updating unitconfigured to update the initial image to a material discriminationimage, using attenuation information corresponding to the at least onematerial and spectrum information for the multi-energy X-ray.

The initial image estimator may estimate the initial image using energydistribution information for each of the at least one material.

The image updating unit may update the initial image further using ahyperparameter associated with the at least one material.

The image updating unit may update the initial image to which acorrection value is applied, for a predetermined number of times, byproviding the initial image as a feedback.

The image updating unit may acquire a correction value for minimizing apredetermined cost function, apply the correction value to the initialimage, and update the initial image to the material discriminationimage.

In still another aspect, there is provided a material discriminationimage generator, the image generator including a receiver configured toreceive a projection image for each energy band generated by passing anX-ray spectrum through an object to be inspected having at least onematerial, an initial image estimator configured to acquire an initialimage for the at least one material based on the projection image, andan acquiring unit configured to acquire a material discrimination imagefor the at least one material by applying an image updating algorithm tothe initial image.

In still another aspect, there is provided a medial image system, themedical image system including a source configured to irradiate amulti-energy X-ray spectrum to an object to be inspected having at leastone material, a material discrimination image processor configured toacquire a material discrimination image for each of the at least onematerial, and a final reconstruction image generator configured togenerate a final reconstruction image by applying a reconstructionalgorithm to a tomographic image including the acquired materialdiscrimination image.

The material discrimination image processor may receive a projectionimage of each energy band generated by passing the X-ray spectrumthrough the object to be inspected having the at least one material, andacquire the material discrimination image for each of the at least onematerial.

The material discrimination image processor may include a receiverconfigured to receive a projection image for each energy band, aninitial image estimator configured to acquire an initial image for eachof the at least one material, and an acquiring unit configured toacquire the material discrimination image for each of the at least onematerial by applying an image updating algorithm to the initial image.

The initial image estimator may acquire the initial image based onenergy distribution information for the at least one material.

In still another aspect, there is provided a medial image systemincluding a source configured to irradiate a multi-energy X-rayspectrum, and a material discrimination image processor configured toreceive projection images for each energy band generated by passing themulti-energy X-ray spectrum through an object to be inspected formed ofat least one material, and to acquire a material discrimination imagefor each of the at least one material.

In still another aspect, there is provided a medial image systemincluding a source configured to irradiate an X-ray spectrum, an X-raydetector configured to classify at least two energy bands, and amaterial discrimination image processor configured to receive projectionimages for each of the detected at least two energy bands and to acquirematerial discrimination images for at least two materials.

In still another aspect, there is provided a medial image systemincluding at least one source configured to irradiate an X-ray spectrumin at least two positions, an X-ray detector configured to classify atleast two energy bands, and a material discrimination image processorconfigured to receive projection images in the at least two positionsand to acquire a single three-dimensional (3D) material discriminationimage or at least two 3D material discrimination images.

In still another aspect, there is provided an image reconstructionprocessing method including acquiring an initial value with respect to atomographic image of an object to be inspected, initializing anauxiliary variable, acquiring a weighted value and an error value, basedon a measured value, transforming a measured image signal, updating theinitialized auxiliary variable using a transform coefficient used totransform the measured image signal, updating the measured value usingthe updated auxiliary variable, the acquired weighted value, and theacquired error value.

Other features and aspects may be apparent from the following detaileddescription, the drawings, and the claims.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a flowchart illustrating an image reconstruction processingmethod according to an example embodiment,

FIG. 2 is a flowchart illustrating an operation of updating an auxiliaryvariable in the image reconstruction processing method of FIG. 1.

FIG. 3 is a flowchart illustrating an operation of updating a measuredvalue in the image reconstruction processing method of FIG. 1.

FIG. 4 is a block diagram illustrating a material discrimination imagegenerator of an image reconstruction processing apparatus, according toan example embodiment.

FIG. 5 is a block diagram illustrating a material discrimination imagegenerator of an image reconstruction processing apparatus, according toanother example embodiment.

FIG. 6 is a block diagram illustrating a medical image system accordingto an example embodiment.

Throughout the drawings and the detailed description, unless otherwisedescribed, the same drawing reference numerals will be understood torefer to the same elements, features, and structures. The relative sizeand depiction of these elements may be exaggerated for clarity,illustration, and convenience.

DETAILED DESCRIPTION

The following detailed description is provided to assist the reader ingaining a comprehensive understanding of the methods, apparatuses,and/or systems described herein. Accordingly, various changes,modifications, and equivalents of the systems, apparatuses and/ormethods described herein will be suggested to those of ordinary skill inthe art. Also, descriptions of well-known functions and constructionsmay be omitted for increased clarity and conciseness.

According to an aspect, provided are an image reconstruction processingmethod and a medical image system employing the image reconstructionprocessing method, in which a tomographic image of an object to beinspected is reconstructed to a final image, using a two-dimensional(2D) projection image of the object that is acquired through an X-ray.

According to another aspect, provided are an image reconstructionprocessing method and a medical image system employing the imagereconstruction processing method, in which a tomographic image of anobject to be inspected that includes a material discrimination image, isreconstructed to a final image, using a 2D projection image of theobject that is acquired through a multi-energy X-ray.

According to still another aspect, provided are an image reconstructionprocessing method and a medical image system employing the imagereconstruction processing method, in which material discrimination of anobject to be inspected is performed using a 2D projection image of theobject that is acquired through a multi-energy X-ray.

An image reconstruction processing apparatus and a medical image systemaccording to example embodiments, may refer to a system using a singleX-ray source or at least two X-ray sources in a single position or in atleast two different positions, and/or using a source for fast switchinga voltage, and/or using a source where an anode formed of at least twomaterials is used, and/or using a source including a filter that isformed of at least two materials and that is located in a front portionthereof, and/or using an X-ray detector for detecting at least twoenergy bands for each of the at least two energy bands. The imagereconstruction processing apparatus and the medical image system may beimplemented, for example, as a radiography system, a tomosynthesissystem, a Computed Tomography (CT) system, and a non-destructiveinspection device. The implementations described are merely examples,and accordingly, it is understood that other implementations arepossible and a multi-energy X-ray based system based on teachings hereinmay be utilized in various applications.

As illustrative examples, provided are an image reconstructionprocessing method for reconstructing a tomographic image of an object tobe inspected to a final image, by using a two-dimensional (2D)projection image of the object that is acquired through an X-ray, animage reconstruction processing method for reconstructing a tomographicimage of an object to be inspected including a material discriminationimage to a final image, by using a 2D projection image of the objectthat is acquired through a multi-energy X-ray, an image reconstructionprocessing method for performing material discrimination of an object tobe inspected, by using a 2D projection image of the object that isacquired through a multi-energy X-ray.

The above described field may be illustrated by the following Equation1.

$\begin{matrix}{{\underset{x}{\arg\;\min}\mspace{14mu} x^{T}W^{T}{Wx}} - {2x^{T}W^{T}b_{0}}} & \lbrack {{Equation}\mspace{14mu} 1} \rbrack\end{matrix}$

In Equation 1, x denotes a target to be reconstructed using a vector,and W and b respectively denote a matrix and a vector that aredetermined based on a predetermined reconstruction scheme. To performmore stable and accurate reconstruction under a condition ofinsufficient data and relatively high noise, neighboring pixelinformation regarding neighboring pixels may be used. A Total Variation(TV) regularization scheme may preserve edge information while using theneighboring pixel information. Equation 2 may be obtained by using theTV regularization scheme with respect to Equation 1, as follows.

$\begin{matrix}{{\underset{x}{\arg\;\min}\mspace{14mu} x^{T}W^{T}{Wx}} - {2x^{T}W^{T}b_{0}} + {2\lambda{x^{I}}_{TV}}} & \lbrack {{Equation}\mspace{14mu} 2} \rbrack\end{matrix}$

In Equation 2, x^(I) denotes an image to be reconstructed, using amatrix. Equation 2 may be obtained by adding a TV norm to Equation 1.The following Equation 3 or Equation 4 may be selectively used for a TVnorm in a 2D problem.

$\begin{matrix}{\mspace{79mu}{{x^{I} \in R^{m \times n}},{{x^{I}}_{{TV}_{I}} = {{\sum\limits_{i = 1}^{m - 1}{\sum\limits_{j = 1}^{n - 1}\sqrt{( {x_{i,j} - x_{{i + 1},j}} )^{2} + ( {x_{i,j} - x_{i,{j + 1}}} )^{2}}}} + {\sum\limits_{i = 1}^{m - 1}{{x_{i,n} - x_{{i + 1},n}}}} + {\sum\limits_{j = 1}^{n - 1}{{x_{m,j} - x_{m,{j + 1}}}}}}}}} & \lbrack {{Equation}\mspace{14mu} 3} \rbrack \\{\mspace{79mu}{{x^{I} \in R^{m \times n}},{{x^{I}}_{{TV}_{L_{1}}} = {{\sum\limits_{i = 1}^{m - 1}{\sum\limits_{j = 1}^{n - 1}\{ {{{x_{i,j} - x_{{i + 1},j}}} + {{x_{i,j} - x_{i,{j + 1}}}}} \}}} + {\sum\limits_{i = 1}^{m - 1}{{x_{i,n} - x_{{i + 1},n}}}} + {\sum\limits_{j = 1}^{n - 1}{{x_{m,j} - x_{m,{j + 1}}}}}}}}} & \lbrack {{Equation}\mspace{14mu} 4} \rbrack\end{matrix}$

Equation 2 may be further generalized. For example, a coefficient of apredetermined transform, such as a wavelet transform, instead of animage value x in Equation 2 may be substituted with an unknown number.Here, a problem may be expressed as given in Equation 5.

$\begin{matrix}{\underset{\theta}{\arg\;\min}( {{\theta^{T}\Phi^{*}W^{T}W\;{\Phi\theta}} - {2\theta^{T}\Phi^{*}W^{T}b_{0}} + {2{\sum\limits_{i}{\lambda_{i}{\theta_{i}^{I}}_{TV}}}}} )} & \lbrack {{Equation}\mspace{14mu} 5} \rbrack\end{matrix}$

In Equation 5, Φ denotes a predetermined transform, and Φ* denotes aHermitian operation of the transform Φ. Additionally, θ denotes acoefficient of the transform Φ using a vector, and θ_(i) is a portion ofθ. For example, when Φ denotes a wavelet reverse transform, θ_(i) maydenote an i-th sub-band. A feature of Equation 5 is that aregularization coefficient λ with different intensities for each portionof θ is used. In addition, Equation 5 may be obtained by generalizingEquation 2. In an example in which Φ=I, Equation 5 may be equivalent toEquation 2.

To simplify Equation 5, Equation 6 may be introduced as below.A=WΦ  [Equation 6]

In Equation 6, A denotes an operator obtained by combining an operationW of Equation 2 with the predetermined transform Φ of Equation 5.Equation 7 may be obtained by rewriting Equation 5 using Equation 6, asbelow.

$\begin{matrix}{\underset{\theta}{\arg\;\min}( {{\theta^{T}A^{*}A\;\theta} - {2\theta^{T}A^{*}b_{0}} + {2{\sum\limits_{i}{\lambda_{i}{\theta_{i}^{I}}_{TV}}}}} )} & \lbrack {{Equation}\mspace{14mu} 7} \rbrack\end{matrix}$

Problems such as Equations 2, 5, and 7 may be regarded as TVminimization problems. When the TV minimization problems are solved orimproved, edge information may be better preserved while the neighboringpixel information is used. However, in a tomography reconstructionproblem, it is difficult to restrict noise using a known TV minimizationscheme, due to a large amount of data. However, since a gradient existsin a dual problem of the TV minimization problem, a gradient-based TVminimization scheme may be applied.

In the dual problem of the TV minimization problem, a dual variable fordescribing a desired x continues to be updated, to finally obtain x. Inexamples and embodiments illustrated herein, a description may beprovided based on 2D. However, it is understood that teachings providedherein may extended to embodiments with other than 2D, for example, to3D.

It is assumed that

is a set of matrix pairs (p,q) satisfying the following condition. (p,q)denotes a matrix satisfying pε

^((m−1)×n), and qε

^(m×(n−1)) In the example, values of (p, q) are to satisfy the followingconditions as given in Equation 8.p _(i,j) ² +q _(i,j) ²≦1,i=1, . . . ,(m−1),j=1, . . . ,(n−1) |p_(i,j)|≦1,|q _(i,j)|≦1  [Equation 8]

A gradient and a divergence operation of a discrete signal may bedefined as given in Equation 9 below. To reconstruct a tomographicimage, a gradient operation and divergence operation may be performedwith respect to each material forming the tomographic image.

Divergence operation for (p,q):

(p,q)→

^(m×n),

(p,q)_(i,j) =p _(i,j) −p _(i−1,j) +q _(i,j) −q _(i,j−1)

Gradient operation for x:

^(T)(x)=(p,q), p _(i,j) =x _(i,j) −x _(i+1,j) q _(i,j) =x _(i,j) −x_(i,j+1)  [Equation 9]

A dual problem of Equation 7 may be induced as given in Equation 10below.

$\begin{matrix}{{\underset{\theta}{\arg\;\min}\mspace{11mu}\underset{({p,q})}{\arg\;\max}{{\theta - {\Phi^{+}( {\hat{x} + {( {W^{T}W} )^{- 1}( {b_{0} - {{\Phi\lambda}\;{vec}\{ {\mathcal{L}( {p,q} )} \}}} )}} )}}}_{2}^{2}} - {{b - {( A^{+} )^{*}\lambda\;{vec}\{ {\mathcal{L}( {p,q} )} \}}}}_{2}^{2}} & \lbrack {{Equation}\mspace{14mu} 10} \rbrack\end{matrix}$

In Equation 10, vec denotes a change of a value stored in a 2D matrix toa vector form. Φ⁺ and A⁺ respectively denote a pseudo-inverse of Φ andoperator A. In the case of a wavelet transform, Φ may denote an operatorfor transforming a wavelet coefficient into an image signal, and Φ⁺ maydenote an operator for transforming an image signal into a waveletcoefficient. A⁺ may be expressed as given in Equation 11 below.A ⁺=Φ⁺ W ⁻¹=(Φ*Φ)⁻¹ Φ*W ⁻¹  [Equation 11]

An algorithm to solve Equation 10 may be induced as given in Equation 12below.(p ^((k+1)) ,q ^((k+1)))=(p ^((k)) ,q ^((k)))+c·

^(T)unvec{λ{circumflex over (θ)}^((k))}{circumflex over (θ)}^((k)) =P_(C){Φ⁺({circumflex over (x)} ^((k)))}{circumflex over (x)} ^((k+1))={circumflex over (x)} ^((k))+(W ^(T) W)⁻¹(b ₀−Φλvec{

(p ^((k+1)) ,q ^((k+1)))}))∥₂ ²  [Equation 12]

In Equation 12, λ{circumflex over (θ)}^((k)) denotes a vector obtainedby multiplying θ_(i) that is a portion of θ by λ_(i). Unvec{ } signifiesthat an image signal stored in a vector is changed in a 2D matrix formand the changed image signal is stored. Pc{ } denotes an operation ofappropriately normalizing, scaling, or thresholding a signal.

Equation 12 provides a scheme to solve Equation 5 obtained bygeneralizing Equation 2. To apply the scheme to a tomography field, Wand b₀ are defined again.

In the field of tomography, a reconstruction scheme includes a maximumlikelihood-expectation maximization (ML-EM) scheme, an ML-convex scheme,a simultaneous algebraic reconstruction technique (SART) scheme, an ARTscheme, and the like. Such reconstruction scheme may be interpreted asan algorithm used to solve Equation 1. For example, the ML-convex schememay enable repetitive computation of a problem where W and b₀ inEquation 13 are substituted into Equation 1.

$\begin{matrix}{\mspace{79mu}{{{( {W^{T}W} )_{i,j} = {{\frac{1}{{\hat{x}}_{i,j}}{\sum\limits_{i}l_{ij}}} < l_{i}}},{\hat{x} > {d_{i}{\exp( {{- {< l_{i}}},{\hat{x} >}} )}}}}{b_{{0i},j} = {{( {W^{T}W} )_{i,j}{\hat{x}}_{i,j}} + {\sum\limits_{i}{l_{ij}( {Y_{i} - {d_{i}{\exp( {{- {< l_{i}}},{\hat{x} >}} )}}} )}}}}}} & \lbrack {{Equation}\mspace{14mu} 13} \rbrack\end{matrix}$

In Equation 13, i denotes an index of a detector, and j denotes a voxelindex of an object to be inspected for reconstruction. Additionally,<l_(i), x> denotes an integration for a ray connecting an i-th detectorto a source, that is, denotes, for example, a Radon transform. Thel_(ij) denotes a length of an i-th line passing through a j-th voxel,and

$\sum\limits_{i}{l_{ij}(\bullet)}$denotes a back-projection that is a transpose operation of the Radontransform. An ML-EM algorithm, a SART algorithm, and an ART algorithmcan also be interpreted with Equation 13 and obtained. When Equation 13is substituted into the algorithm described in Equation 12, ML-EM,ML-convex, ART, and SART included in the TV regularization may bereconstructed.

Equation 13 may be obtained by performing approximation using asecondary Taylor series, in a numerical formula obtained by simplifyinga Poisson log-likelihood function using approximation of a monochromaticradiation. The monochromatic radiation refers to a situation where amonochromatic X-ray is generated. A large number of known reconstructionalgorithms induce W and b, under assumption of the monochromaticradiation as shown in Equation 13. Also, ML-EM and SART may be used tosimplify a data acquisition model under assumption of the monochromaticradiation, despite numerical formula being different in form from eachother. However, in most X-ray sources used in image diagnosis ornondestructive inspection, polychromatic radiation may occur. In otherwords, polychromatic X-rays may be radiated from X-ray sources.According to an embodiment, a reconstruction scheme proposed in thepresent disclosure enables reconstruction of a final image based on anX-ray source with a polychromatic radiation characteristic, and W and bmay be computed using the data acquisition model of polychromaticradiation.

A system based on a simulated single energy or multi-energy X-ray may beexpressed as given in Equation 14 below.

$\begin{matrix}{{Y_{j}( r_{s} )} = {{\int_{E_{j\; s}}^{E_{j\; ɛ}}{{I_{j}(ɛ)}{\exp( {- {\oint_{P_{s}}{{\mu( {x,y,z,ɛ} )}{\mathbb{d}p}}}} )}{\mathbb{d}ɛ}}} + {n( r_{s} )}}} & \lbrack {{Equation}\mspace{14mu} 14} \rbrack\end{matrix}$

In Equation 14, Y denotes a measured image of a system based on amulti-energy X-ray measured in a j-th energy band. Additionally, Idenotes a known function based on an influence of a source irradiated toan object to be inspected and a response influence of a detector, andincludes spectrum information of a system based on a multi-energy X-ray.F denotes a function (x and E) based on an influence of a compositionratio of materials forming an object to be inspected in a correspondingenergy band. Furthermore, j denotes an index of an energy band, and rdenotes an N-dimensional position vector, for example, (x, y) in thecase of a 2D image, (x, y, z) in the case of a 3D image, and the like.For example,

${F_{j}( {x,E} )} = {\sum\limits_{i}{{\mu_{i}( E_{k} )}L_{i}}}$may be obtained. E denotes an energy variable, and n denotes a noiseterm.

To solve Equation 14, the Poisson log-likelihood may be maximized Sincean operation of the Poisson log-likelihood is complex, it is difficultto induce a solution for maximizing the Poisson log-likelihood withoutusing approximation of monochromatic radiation. However, complexity maybe reduced if commonality between the Poisson log-likelihood and aKullback-Leibler (KL) divergence, that are mathematically proven, isused. The KL divergence may be expressed as given in Equation 15.

$\begin{matrix}{{{KL}(x)} = {{\sum\limits_{k,i,E}( {{d^{(k)}(i)}\frac{{\hat{q}}^{(k)}( {i,E} )}{\sum\limits_{E^{\prime}}{{\hat{q}}^{(k)}( {i,E^{\prime}} )}}} )} + {\sum\limits_{k,i,E}( {{I^{(k)}( {i,E} )}{\exp( {{{- {\sum\limits_{m}{\mu_{m}(E)}}} < l_{i}},{x_{m} >}} )}} )}}} & \lbrack {{Equation}\mspace{14mu} 15} \rbrack\end{matrix}$

In Equation 15, k denotes an index indicating an energy spectrum, andmay have a value greater than 1. Additionally, j denotes a voxel indexof an object to be inspected for reconstruction. Furthermore, i denotesan index of a detector, and d(i) denotes a data value detected from ani-th pixel of the detector. The <l_(i), x> denotes an integration for aray connecting an i-th detector to a source, that is, denotes, forexample, a Radon transform. In addition, m denotes an index of anattenuation curve μ_(m)(E), and may have a value greater than 1. InEquation 15, x signifies information to be reconstructed. The x_(m)denotes a subset of x, and may be interpreted as an object to beinspected that is formed of materials corresponding to m. The I(i,E)denotes an X-ray spectrum. When an attenuation phenomenon does notoccur, I(i,E) denotes a number of X-ray photons of E-energy physicallyreaching an i-th detector pixel, q(i,E) denotes a monochromatic modelfor an i-th pixel and may be defined as given in Equation 16 below.

$\begin{matrix}{{{\hat{q}}^{(k)}( {i,E} )} = {{I^{(k)}( {i,E} )}{\exp( {{{- {\sum\limits_{m}{\mu_{m}(E)}}} < l_{i}},{\hat{x} >}} )}}} & \lbrack {{Equation}\mspace{14mu} 16} \rbrack\end{matrix}$

When an x for minimizing the KL divergence is found by approximating anx using the secondary Taylor series and by updating the approximated x,Equation 15 may become equivalent to a problem of Equation 1. Here, Wand b may be calculated by the following Equation 17:

$\begin{matrix}{\mspace{79mu}{{( {W^{T}W} )_{ij} = {\sum\limits_{k}{\sum\limits_{i}{l_{ij}{\sum\limits_{E}{{{\hat{q}}^{(k)}( {i,E} )}{\mu(E)}{\mu(E)}^{T}}}}}}}{b_{0_{i,j}} = {{( {W^{T}W} )_{i,j}{\hat{x}}_{i,j}} + {\sum\limits_{k}{\sum\limits_{i}{{l_{ij}( {1 - \frac{d^{(k)}(i)}{{\hat{d}}^{(k)}(i)}} )}{\sum\limits_{E}{{{\hat{q}}^{(k)}( {i,E} )}{\mu(E)}}}}}}}}}} & \lbrack {{Equation}\mspace{14mu} 17} \rbrack\end{matrix}$

In Equation 17,

$\sum\limits_{i}{l_{ij}(\bullet)}$denotes a back-projection that is a transpose operation of the Radontransform.

An image processing method based on a polychromatic model may be inducedby combining Equation 12 and Equation 17.

In an example in which at least two different X-ray spectrums areemitted in a single position and measured by a detector, or in anotherexample in which a single X-ray spectrum or at least two different X-rayspectrums are emitted in a single position and measured by a detectorenabling energy classification, a scheme of combining Equation 12 andEquation 17 may be used to discriminate materials. Here, since an imageto be reconstructed may become 2D image, there is no need to perform

$\sum\limits_{i}{{l_{ij}(\bullet)}.}$Additionally, in the examples, a multi-energy X-ray radiography, amammography, and the like may be used.

In still another example in which a projection image is obtained in aplurality of different positions and a single X-ray spectrum is used, animage without a beam hardening artifact may be reconstructed using asingle attenuation curve (m=1).

In still another example in which a projection image is obtained in aplurality of different positions, and when a single X-ray spectrum isused, a 3D image without a beam hardening artifact may be reconstructedusing a single attenuation curve (m=1), and a 3D image where materialsare discriminated may be reconstructed using at least two attenuationcurves (m>1). The scheme of using at least one X-ray spectrum mayinclude, for example, a scheme of using at least two X-ray sources,and/or a scheme of fast switching a voltage applied to a source, and/ora scheme of forming an anode of a source using at least two materials,and/or a scheme of forming a filter using at least two materials andlocating the filter in a front end of a source, and the like.

Through the above schemes, a tomographic image of an object to beinspected can be reconstructed to a final image, by using a 2Dprojection image of the object that is acquired through an X-ray.Additionally, a tomographic image of an object to be inspected thatincludes a material discrimination image can be reconstructed to a finalimage, by using a 2D projection of the object that is acquired through amulti-energy X-ray.

Furthermore, material discrimination of an object to be inspected can beperformed, by using a 2D projection image of the object that is acquiredthrough a multi-energy X-ray.

According to an embodiment, a tomographic image of a predeterminedobject to be inspected may be reconstructed, or material discriminationfor the object may be performed, by computing an initial value withrespect to the tomographic image, by initializing an auxiliary variable,by computing a weighted value and an error value based on a measuredvalue, by performing a transform enabling a multi-resolution analysis onthe measured value, by updating the auxiliary variable using a transformcoefficient of the measured value, and by updating the measured valueusing the updated auxiliary variable, the weighted value, and the errorvalue. Aspects the above operations may be repeated accordingly toreconstruct the tomographic image and perform the materialdiscrimination.

FIG. 1 illustrates an image reconstruction processing method accordingto an example embodiment.

Referring to FIG. 1, in operation 101, an initial value with respect toa tomographic image of a predetermined object to be inspected may becomputed, and an auxiliary variable “(p,q)” may be initialized.

In operation 102, a weighted value and an error value may be computedbased on a measured value.

For example, a weighted value “(W^(T)W)⁽⁻¹⁾” and an error value “b₀” maybe computed based on a secondary Taylor series approximation of aKullback-Leibler (KL) divergence function corresponding to a Poissonlog-likelihood function.

As another example, a weighted value “(W^(T)W)⁽⁻¹⁾” and an error value“b₀” may be computed using one or more of an ML-EM algorithm based on amonochromatic radiation model, an ML-convex algorithm, and a SARTalgorithm.

In operation 103, a measured image signal may be transformed. Here, atransform scheme enabling a multi-resolution analysis may be applied.

In operation 104, the initialized auxiliary variable “(p,q)” may beupdated using a transform coefficient used to transform the measuredimage signal.

In operation 105, the measured value may be updated using the updatedauxiliary variable “(p,q)”, the computed weighted value, and thecomputed error value.

In the example image reconstruction processing method, to transform themeasured image signal so that the multi-resolution analysis is enabled,one or more of a wavelet transform, a contourlet transform, a curvelettransform, a shearlet transform, a bandelet transform, and a ridgelettransform may be used.

In operation 106, whether to repeat operations 102 to 105 may bedetermined. When operations 102 to 105 are determined to be repeated,the image reconstruction processing method may return to operation 102.When operations 102 to 105 are not repeated, the image reconstructionprocessing method may be completed after the updating of the measuredvalue in operation 105.

FIG. 2 further illustrates the operation 104 of the image reconstructionprocessing method of FIG. 1.

Referring to FIG. 2, in operation 201, the transform coefficient of themeasured value may be multiplied by a weighted value “λ” for eachportion. In operation 202, a gradient operation may be performed on thetransform coefficient multiplied by the weighted value “λ”.

In operation 203, the transform coefficient where the gradient operationis performed may be multiplied by an appropriate value, for example, aweighted value “c”, and a current auxiliary variable “(p,q)” may beadded thereto. Thus, the auxiliary variable “(p,q)” may be updated.

FIG. 3 further illustrates the operation 105 of the image reconstructionprocessing method of FIG. 1.

Referring to FIG. 3, in operation 301, a divergence operation may beperformed on the updated auxiliary variable “(p,q)”.

In operation 302, weighting may be performed by multiplying, by theweighted value “λ”, the auxiliary variable “(p,q)” where the divergenceoperation is performed, for each portion. In operation 303, theauxiliary variable “(p,q)” multiplied by the weighted value “λ” may betransformed into an image domain, and transformed into an image signal.

In operation 304, a result of the operation 302 may be subtracted fromthe error value, and a value obtained by the subtracting may bemultiplied by the weighted value “c” again. In operation 305, a resultof the operation 304 may be added to the measured value. Accordingly,the measured value may be updated.

FIG. 4 illustrates a material discrimination image generator 400 of animage reconstruction processing apparatus according to an exampleembodiment.

The material discrimination image generator 400 of FIG. 4 includes aninitial image estimator 410, a storage unit 420, and an image updatingunit 430.

For example, the initial image estimator 410 receives projection imagesE₁ to E_(N) for each energy band generated by passing a multi-energyX-ray spectrum through an object that is to be inspected and that isformed of at least one material, and generate initial images for each ofM materials forming the object. The initial image estimator 410 mayestimate the initial images using energy distribution information foreach of the at least one material of the object.

The storage unit 420 records, for example, in a table form, attenuationinformation I_(A) corresponding to the at least one material, andspectrum information I_(S) for the multi-energy X-ray.

The image updating unit 430 updates the initial images to which thecorrection value is applied, for a predetermined number of times, byproviding the initial images as feedback.

The attenuation information I_(A) and the spectrum information I_(S)recorded in the storage unit 420 may be input to the image updating unit430, and may be used to update the initial images output from theinitial image estimator 410.

The image updating unit 430 may update the initial images to a materialdiscrimination image by further using a hyperparameter associated withthe material. Here, the hyperparameter may be interpreted as a componentratio of the material.

The spectrum information I_(S) stored in the storage unit 420 may berecorded in an external storage device in another implementation. Forexample, the storage unit 420 may be merely logically referred to, thatis, does not refer to a physical location where correspondinginformation is actually recorded.

The image updating unit 430 may update the initial images to a materialdiscrimination image, using the initial images estimated by the initialimage estimator 410 and the spectrum information I_(S) and attenuationinformation I_(A) recorded in the storage unit 420.

An image updating procedure performed by the image updating unit 430 mayemploy a scheme of computing a correction value for minimizing apredetermined cost function, applying the correction value to theinitial images, and updating the initial images to the materialdiscrimination image. According to an embodiment, the image updatingunit 430 may perform pixel-by-pixel updating based on pixels of animage. According to another embodiment, the image updating unit 430 mayperform block-by-block updating, or according to still anotherembodiment, perform image-by-image updating. Accordingly, while theoperation of the image updating unit 430 is described, for example,based on the pixel-by-pixel updating, it is understood thatimplementations are not limited thereto.

FIG. 5 illustrates a material discrimination image generator 500 of animage reconstruction processing apparatus according to another exampleembodiment.

The material discrimination image generator 500 of FIG. 5 includes areceiver 510, an initial image estimator 520, and an acquiring unit 530.

For example, the receiver 510 receives projection images for each energyband. The initial image estimator 520 estimates initial images for eachmaterial based on the projection images.

The acquiring unit 530 acquires a material discrimination image for eachmaterial by applying an image updating algorithm to the initial images.

FIG. 6 illustrates a medical image system 600 according to an exampleembodiment.

The medical image system 600 includes a source 610, a materialdiscrimination image processor 620, and a final reconstructed imagegenerator 630.

For example, the source 619 irradiates a multi-energy X-ray spectrum toan object to be inspected. The material discrimination image processor620 acquires a material discrimination image for each of materialsforming the object. As an example, the material discrimination imageprocessor 620 may receive a projection image of each energy bandgenerated by passing the multi-energy X-ray spectrum through an objectthat is to be inspected and that is formed of at least one material, andmay acquire a material discrimination image for each of the at least onematerial.

According to an aspect, the material discrimination image processor 620may include a receiver to receive projection images for each energyband, an initial image estimator to estimate initial images for each ofthe materials, and an acquiring unit to acquire a materialdiscrimination image for each material by applying an image updatingalgorithm to the initial images. The initial image estimator mayestimate the initial images based on energy distribution information foreach material.

In the example of FIG. 6, the final reconstructed image generator 630generates a final reconstructed image by applying a repeatingreconstruction algorithm to a tomographic image including the acquiredmaterial discrimination image.

The processes, functions, methods and/or software described herein maybe recorded, stored, or fixed in one or more non-transitorycomputer-readable media including program instructions to be implementedby a computer to cause a processor to execute or perform the programinstructions. The media may also include, alone or in combination withthe program instructions, data files, data structures, and the like. Theprogram instructions recorded on the media may be those speciallydesigned and constructed for the purposes of the example embodiments, orthey may be of the kind well-known and available to those having skillin the computer software arts. Examples of non-transitorycomputer-readable media include magnetic media such as hard disks,floppy disks, and magnetic tape; optical media such as CD ROM disks andDVDs; magneto-optical media such as optical disks; and hardware devicesthat are specially configured to store and perform program instructions,such as read-only memory (ROM), random access memory (RAM), flashmemory, and the like. Examples of program instructions include bothmachine code, such as produced by a compiler, and files containinghigher level code that may be executed by the computer using aninterpreter. The described hardware devices may be configured to act asone or more software modules that are recorded, stored, or fixed in oneor more non-transitory computer-readable media, in order to perform theoperations of the above-described example embodiments, or vice versa. Inaddition, a computer-readable medium may be distributed among computersystems connected through a network and computer-readable codes orprogram instructions may be stored and executed in a decentralizedmanner.

According to certain example(s) described above, according to an aspect,a tomographic image may be reconstructed while satisfying a simplealgorithm with high accuracy.

According to another aspect, a reconstruction performance may beimproved even in a low dose environment, by using information ofneighboring pixels.

According to another aspect, materials may be discriminated moreefficiently even in a 2D multi-energy X-ray system.

According to another aspect, ML may be estimated accurately without anapproximation of monochromatic radiation in a 3D tomosynthesis.

According to another aspect, 3D reconstruction may be performed moreefficiently without a beam hardening artifact in a 3D tomosynthesis.

According to another aspect, 3D material discrimination may be performedmore efficiently in a tomography using a 3D multi-energy.

According to another aspect, when a tissue of a living body such as ahuman body is to be inspected, data such as a Bone Mineral Density(BMD), a Total Body Fat (TBF), a Total Body Water (TBW), and the likecan be measured.

According to another aspect, an X-ray image with high quality and highcontrast may be obtained using a medical image apparatus according toteachings herein.

According to another aspect, a material discrimination image applicableto a conventional dual energy CT may be obtained.

According to another aspect, aliasing and artifacts may be preventedfrom occurring in a tomographic image in a limited angle that isobtained from an object to be inspected.

According to another aspect, an amount of information used in synthesisof a tomographic image may be reduced, and accordingly, an amount ofradiation exposure for an object to be inspected may be reduced.

According to another aspect, a number of viewpoint images used insynthesis of a tomographic image may be reduced, and accordingly, acapturing time may be reduced.

According to another aspect, blurring in a depth direction using arepeating reconstruction algorithm may be reduced.

According to another aspect, an artifact with respect to a sparseviewpoint may be dealt with more robustly.

According to another aspect, a complex L1 minimization problem and a TVregularization problem may be processed more quickly, using a modifiedrepeating reduction algorithm, and acceleration may be possible using aGeneral Processing Unit (GPU).

A number of examples have been described above. Nevertheless, it will beunderstood that various modifications may be made. For example, suitableresults may be achieved if the described techniques are performed in adifferent order and/or if components in a described system,architecture, device, or circuit are combined in a different mannerand/or replaced or supplemented by other components or theirequivalents. Accordingly, other implementations are within the scope ofthe following claims.

What is claimed is:
 1. A material discrimination image generatorcomprising: an initial image estimator configured to receive aprojection image for each energy band generated by passing amulti-energy X-ray spectrum through an object to be inspected having amaterial and to generate an initial image for the material by combininginformation of the projection image of each energy band; and an imageupdating unit configured to update the initial image to a materialdiscrimination image, using attenuation information corresponding to thematerial and spectrum information for the multi-energy X-ray.
 2. Thematerial discrimination image generator of claim 1, wherein the initialimage estimator estimates the initial image using energy distributioninformation for the material.
 3. The material discrimination imagegenerator of claim 1, wherein the image updating unit updates theinitial image further using a hyperparameter associated with thematerial.
 4. The material discrimination image generator of claim 1,wherein the image updating unit updates the initial image, to which acorrection value is applied, for a predetermined number of times byproviding the initial image as feedback.
 5. The material discriminationimage generator of claim 1, wherein the image updating unit acquires acorrection value for minimizing a predetermined cost function, appliesthe correction value to the initial image, and updates the initial imageto the material discrimination image.
 6. A material discrimination imagegenerator comprising: a receiver configured to receive a projectionimage for each energy band generated by passing an X-ray spectrumthrough an object to be inspected having a material; an initial imageestimator configured to acquire an initial image for the material bycombining information of the projection image of each energy band; andan acquiring unit configured to acquire a material discrimination imagefor the material by applying an image updating algorithm to the initialimage.
 7. A medical image system comprising: a source configured toirradiate a multi-energy X-ray spectrum to an object to be inspectedhaving a material; a receiver configured to receive a projection imagefor each energy band of the multi-energy X-ray spectrum; an initialimage estimator configured to acquire an initial image for the materialby combining information of the projection image for each energy band;an acquiring unit configured to acquire a material discrimination imagefor the material by applying an image updating algorithm to the initialimage; and a final reconstruction image generator configured to generatea final reconstruction image by applying a reconstruction algorithm to atomographic image including the acquired material discrimination image.8. The medical image system of claim 7, wherein the initial imageestimator acquires the initial image based on energy distributioninformation for the material.